# Math 2B, College of the Desert

 Linear Equation Linear Equation: x,y,z; more generally define a linear equation in the n variables x1, x2, . . . . , xn to be one that can be expressed in the form a1x1+a2x2+. . . +anxn. Homogeneous Linear Equation Homogeneous Linear Equation: b = 0[in the variables x1,x2 . . .xn]. System of linear equations System of linear equations: A finite set of linear equations or, more briefly, a linear system. Variables Variables: Unknownsie:x, y, z . . . . .orx1, x2, x3 . . . . Ordered n-tuple Ordered n-tuple:(s1, s2, . . . . , sn) N = 2 N = 2: Called an ordered pair, for ordered n-tuple. N = 3 N = 3: Called an ordered triple, for ordered n-tuple. Consistant Consistant: Has at least one solution if not infinite. Inconsistant Inconsistant: Has no solutions. Parameter Parameter: Substitution of a veriable with another (different) variable.ie:X = t Parameter equations Parameter equations: All the variables are substituted with a different variable (one not used yet). Augmented Matrix Augmented Matrix: Just putting the equations into matrix form. Algebraic Operations Algerbraic Operations: 1. Multiply row by non-0 constant.2. Interchange 2 rows.3. Add a constant times 1 row to another. Unique solution Unique solution: One solution. Theorem 1.4.1 Theorem 1.4.1:a)A+B=B+A Communatative Law additionb)A+(B+C)=(A+B)+C Associative Law addc)A(BC)=(AB)C Associative Law Multid)A(B+C)=AB+AC left distributive Multie)(B+C)A=BA+CA Right distributive Multif)A(B-C)=AB-ACg)(B-C)A=BA-CAh)a(B+C)=aB+aCi)a(B-C)=aB-aCj)(a+b)C=aC+bCk)(a-b)C=aC-bCl)a(bC)=(ab)Cm)a(BC)=aB(C)=B(aC) Theorem 1.4.2 Theorem 1.4.2: If c is a scalar, and if the sizes of the matrix are such that the operations can be performed, then:a) A+0=0+A=Ab)A-0=Ac)A-A=A+(-A)=0d)0A=0e)If cA=0, then c=0 or A=0 Theorem 1.4.3 Theorem 1.4.3: If R is the reduced row echelon form of an nxn matrix A, then either R has a row of zeros or R is the Identity Matrix In. AuthorMattyj1388 ID81586 Card SetMath 2B, College of the Desert DescriptionElementary Linear Algerbra: Howard Anton / Chris Rorres Updated2011-06-23T22:26:48Z Show Answers